Modeling of Darcy‐Forchheimer magnetohydrodynamic Williamson nanofluid flow towards nonlinear radiative stretching surface using artificial neural network

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Abstract
Modern industries face a new challenge in cooling processes. Traditional cooling lubricants have limited heatconducting capacity. The development of nanofluids possessing superior properties such as high thermal conductivity, homogeneity, and long‐term stability has revolutionized the cooling lubrication industry. The literature reports a wide range of applications of nanofluid, such as cooling devices, peristaltic pumps for diabetic treatments, accelerators, reactors, petroleum industry applications, solar collectors and so forth. Nanofluids like Williamson nanofluid are very important non‐Newtonian fluids that have pseudoplastic properties. Williamson nanofluid has a number of applications in the medical and engineering sciences. It is used in food processing, inkjet printing, adhesives and emulsions, coated photographic films, and many other applications. In the current study, the nanomaterial flow of the Darcy‐Forchheimer Williamson nanofluid model is evaluated using the Levenberg–Marquardt approach with backpropagated neural networks. Thermalphoresis and Brownian motion are incorporated into the nanofluid model. This system is converted into an analogous nonlinear ordinary differential system through the application of necessary transformations. A dataset for the proposed multilayer perceptron artificial neural network is generated by altering the necessary variables through a Runge–Kutta fourth‐order shooting procedure. It has been created an artificial neural network called a multiple‐layer perceptron in order to forecast the values of the multiple‐layer perceptron. It is discovered that the parameter had the highest mean deviation of and the parameter had the lowest mean deviation of . Furthermore, MSE value of ANN model developed to estimate the skin friction coefficient value as and R value as 0.99954 whereas MSE and R values of the ANN model developed for the estimation of the LNN value were obtained as and 0.99999, respectively.

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